   Chapter 2, Problem 154GQ

Chapter
Section
Textbook Problem

Estimating the radius of a lead atom. (a) You are given a cube of lead that is 1.000 cm on each side. The density of lead is 11.35 g/ cm3. How many atoms of lead are in the sample? (b) Atoms are spherical; therefore, the lead atoms in this sample cannot fill all the available space As an approximation, assume that 60% of the space of the cube is filled with spherical lead atoms. Calculate the volume of one lead atom from this information. From the calculated volume (V) and the formula (4/3) πτ3 for the volume of a sphere, estimate the radius (r) of a lead atom.

(a)

Interpretation Introduction

Interpretation: The number of atoms for lead in given sample of lead cube, with each side of value 1cm needed to be calculated.

Concept introduction:

Conversion formula for mass of a molecule and number moles,

Numberofmoles=MassingramsMolarmass

Equation for number of atoms is,

Number of moles×6.022×1023atoms=number of atoms

Equation for density from volume and mass is,

Density=MassVolume

Equation for finding Volume of sphere is,

Volume=(4/3)πr3

Explanation

The side of the lead cube is given that 1cm.

Therefore, the volume of the lead cube is,

(1cm)3=1cm3

The density of the lead cube is given as 11.35g/cm3.

Equation for mass from volume and density is,

Density×Volume=Mass

Therefore, the mass of lead cube is,

11.35g/cm3×1cm3=11.35g

Conversion formula for mass of a molecule and number moles,

Numberofmoles=MassingramsMol

(b)

Interpretation Introduction

Interpretation: The volume of one lead atom and its radius have to be calculated under given conditions.

Concept introduction:

Conversion formula for mass of a molecule and number moles,

Numberofmoles=MassingramsMolarmass

Equation for number of atoms is,

Number of moles×6.022×1023atoms=number of atoms

Equation for density from volume and mass is,

Density=MassVolume

Equation for finding Volume of sphere is,

Volume=(4/3)πr3

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